Calculating height achieved under changing gravitional field

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The discussion centers on calculating the height achieved under a changing gravitational field using the gravitational acceleration equation g = GM/r^2. The integration of this equation leads to the expression v^2/2 = GM/r + C, which is essential for understanding the motion of a projectile in a non-uniform gravitational field. The initial attempt to apply the uniformly accelerated motion equation ?Y = volt + 0.5AT^2 was deemed inappropriate for this scenario. The conversation highlights the complexity of solving for height as a function of time in varying gravitational conditions.

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relativitydude
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For some reason, this is alluding me at the moment. We know the gravitational acceleration equation is g = GM/r^2, integrate that in respect to r to yield -GM/r

I thought I could use

?Y = volt + .5AT^2

and subsitute GM(-1/Ro + 1/R) into A

For some reason this is not working, is my line of reasoning correct?
 
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relativitydude said:
We know the gravitational acceleration equation is g = GM/r^2, integrate that in respect to r to yield -GM/r
Not exactly:
[tex]g = dv/dt = - GM/r^2[/tex]
[tex]v dv/dr = - GM/r^2[/tex]
Now you can integrate with respect to r:
[tex]v^2/2 = GM/r + C[/tex]


I thought I could use

?Y = volt + .5AT^2
That's only good for uniformly accelerated motion.
For some reason this is not working, is my line of reasoning correct?
No. What problem are you trying to solve? The height of a projectile as a function of time? That's not so simple.
 
Thank you very much! :)
 

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